A. Hardesty

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20212024

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math.AC2024

Realizing Algebra Structures on Free Resolutions of Grade 3 Perfect Ideals

Alexis Hardesty

Perfect ideals $I$ of grade $3$ in a local ring $(R, m, k)$ can be classified based on multiplicative structures on $Tor_{∙}^{R} (R / I, k)$ . The classifica…

math.AC2023

Sampling Algebra Structures on Minimal Free Resolutions

Lars Winther Christensen, Orin Gotchey, Alexis Hardesty

Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense…

math.AC2022

The Tor algebra of trimmings of Gorenstein ideals

Luigi Ferraro, Alexis Hardesty

Let $(R, m, k)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric m…